Milan won 1-0 in the Serie A clash at home after an early goal from Samuel Chukwueze, despite being reduced to 10 men following Tijjani Reijnders' red card at the half-hour mark.
"I must say that the game had two parts. The first one until minute 30 when we received a red card," Fonseca told DAZN.
"We played 30 minutes with great personality and quality. It was close to my idea. After the red card, it was a game made of team spirit.
"We suffered, but we suffered together. If there was any doubt on whether this team was united, today we proved we are."
Fonseca stated that his side deserved the win, despite Udinese having two goals disallowed, one from Kingsley Ehizibue and another from Christian Kabasele following the narrowest of offside calls.
"It would have been unfair for the team. We had the best chances and it would have been unfair not to win this game. The team deserved these three points," he said.
He also praised midfielder Christian Pulisic for his effort, including an assist and his defensive work, after Reijnders got sent off.
"Christian's game was fantastic. This is the spirit that we must always have," he said.
For Udinese manager Kosta Runjaic, the night was a bitterly disappointing affair as his side failed to take advantage of their numerical advantage.
"I'm not a referee. I am the coach. It’s senseless to say anything," Runjaic said about the two disallowed goals.
"Even with a man up, it was not easy against a team that defended deep. We needed patience, good passing rhythm and circulation and a bit of luck.
"Surely I don’t like the result because it was possible to go home with a draw."
